A372869 Decimal expansion of the number whose continued fraction coefficients are given in A084580.

5, 8, 1, 5, 8, 0, 3, 3, 5, 8, 8, 2, 8, 3, 2, 9, 8, 5, 6, 1, 4, 5, 0, 0, 6, 0, 7, 2, 2, 8, 0, 6, 5, 5, 2, 4, 7, 7, 6, 3, 0, 5, 6, 6, 9, 6, 2, 0, 0, 9, 2, 3, 0, 1, 3, 6, 2, 1, 2, 1, 5, 5, 5, 1, 5, 7, 6, 7, 1, 0, 4, 9, 1, 2, 4, 1, 9, 5, 3, 4, 0, 8, 9, 4, 9, 2, 0, 1, 2, 6, 9, 4, 1, 4, 2, 1, 2, 9, 0, 9, 2, 8, 0, 5, 9, 2, 1, 2, 8, 8, 7, 8, 6, 1, 7, 6, 8, 0, 8, 0, 4, 1, 3, 2, 1, 3, 6, 3, 7, 5, 7, 8, 3, 2, 6

Offset

0,1

Comments

This constant is normal in the continued fraction sense since its continued fraction coefficients follow the Gauss-Kuzmin distribution by construction. - Jwalin Bhatt, Jan 09 2026

Links

Jwalin Bhatt, Table of n, a(n) for n = 0..10000

Formula

Equals lim_{n->oo} A390651(n) / A390652(n). - Jwalin Bhatt, Jan 09 2026

Example

0.5815803358828329856145006072280655247763056696200923013621215551576710...

Prog

(Python) # Using `sample_gauss_kuzmin_distribution` function from A084580.
from sympy import floor, continued_fraction_convergents
from collections import deque
from os.path import commonprefix
def reliable_digits_from_cf(coeffs, prec):
    frac_lower, frac_upper = deque(continued_fraction_convergents(coeffs+[1]), maxlen=2)
    order = 10**prec
    trunc_lower = floor(frac_lower*order) / order
    trunc_upper = floor(frac_upper*order) / order
    return commonprefix([f'{trunc_lower:.{prec}f}'[2:], f'{trunc_upper:.{prec}f}'[2:]])
num_coeffs = 180
coeffs = [0] + sample_gauss_kuzmin_distribution(num_coeffs)
num = reliable_digits_from_cf(coeffs, prec=200)
A372869 = [int(d) for d in num]

Crossrefs

Cf. A084580 (continued fraction), A390651, A390652.

Sequence in context: A275688 A330867 A193743 * A195356 A263497 A198139

Adjacent sequences: A372866 A372867 A372868 * A372870 A372871 A372872

Keyword

cons,nonn

Author

Jwalin Bhatt, Jul 04 2024

Status

approved